Exact solutions for the static bending of Euler-Bernoulli beams using Eringen’s two-phase local/nonlocal model

By Yuanbin Wang, Xiaowu Zhu, Hui-hui Dai. 2016

186 citations recorded by the source corpus.

Though widely used in modelling nano- and micro- structures, Eringen’s differential model shows some inconsistencies and recent study has demonstrated its differences between the integral model, which then implies the necessity of using the latter model. In this paper, an analytical study is taken to analyze static bending of nonlocal Euler-Bernoulli beams using Eringen’s two-phase local/nonlocal model. Firstly, a reduction method is proved rigorously, with which the integral equation in consideration can be reduced to a differential equation with mixed boundary value conditions. Then, the static bending problem is formulated and four types of boundary conditions with various loadings are considered. By solving the corresponding differential equations, exact solutions are obtained explicitly in all of the cases, especially for the paradoxical cantilever beam problem. Finally, asymptotic analysis of the exact solutions reveals clearly that, unlike the differential model, the integral model adopted herein h...

Subfields: Materials Chemistry, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/f22c24e7ffff0a78248afbfb43759b22c2cbb7d7

Citations in the corpus

• Vibrations of Bernoulli-Euler beams using the two-phase nonlocal elasticity theory (2017, unknown): “This softening effect of the Eringen’s nonlocality has been reported for static bending (Khodabakhshia and Reddy, 2015; Wang et al., 2016), as well as for bending vibrations (Eptaimeros et al., 2016).”